Question

David measures a line to be 8.9 in long. If the actual measurement is 9 in, find David's relative error to the nearest hundredth.

Answer 1

To find David's relative error, we need to use the formula for relative error:

\[
\text{Relative Error} = \frac{|\text{Measured Value} - \text{Actual Value}|}{|\text{Actual Value}|}
\]

In this case, the measured value is 8.9 and the actual value is 9. Let's plug these values into the formula.

1. Calculate the absolute error:
\[
|\text{Measured Value} - \text{Actual Value}| = |8.9 - 9| = |-0.1| = 0.1
\]

2. Calculate the absolute value of the actual value:
\[
|\text{Actual Value}| = |9| = 9
\]

3. Now we can calculate the relative error:
\[
\text{Relative Error} = \frac{0.1}{9}
\]

4. Perform the division:
\[
\frac{0.1}{9} \approx 0.0111111
\]

5. Finally, round to the nearest hundredth:
\[
0.0111111 \approx 0.01
\]

Therefore, David's relative error to the nearest hundredth is:

\[
\boxed{0.01}
\]